The above formulated RT-TDDFT methodology was implemented in the ReSpect program, [1]} and used to investigate the
TAS spectra of two prototypical molecules, ethylene and thiophene at the valence and core (L\(_{2,3}\) ) energy region, respectively, employing 1c non-relativistic, 2c amfX2C and 4c Dirac–Coulomb Hamiltonian. Geometries of the systems are given in SI.
Uncontracted aug-cc-pVXZ basis set (X=T(C), D(H) for ethylene and T(S), D(C,H) for thiophene) [2]}, [3]}, [4]}, [5]} with PBE0–40HF hybrid xc functional [6]} including 40% exact exchange contributions is used. [7]}
For core absorption processes, we use the selective perturbation scheme described above,
whereby only electric dipole moment contributions originating from the core S \(2p_{1/2}\)  and \(2p_{3/2}\)  orbitals are considered to be dipole-allowed. [8]}
The details of the TAS computational setup are elucidated in Table REF  and  Figure S1.
Note that the choice of direction of polarization of pump pulse (\(\mathbf {n}\) ) is important as the spectra are sensitive to geometrical features.
<TABLE><FIGURE>